Global survey of star clusters in the Milky Way: VII. Tidal parameters and mass function - Just, Andreas; Piskunov, A. E.; Klos, J. H.; Kovaleva, D. A.; Polyachenko, E. V. (Astronomy and astrophysics, 2023)
Aims. We built Galactic open star cluster mass functions (CMFs) for different age sub-samples and spatial locations in the wider solar neighbourhood. Here, we present a simple cluster formation and evolution model to reproduce the main features of the CMFs. Methods. We used an unbiased working sample of 2227 clusters of the Milky Way Star Cluster (MWSC) catalogue, which occupy the heliocentric cylinders with magnitude-dependent completeness radii of 1–5 kpc. The MWSC survey provides an extended set of open star cluster parameters, including tidal radii, distances, and ages. From an analytic three-component Galaxy model, we derived tidal masses of clusters with a typical accuracy of about 70%. Our simple model includes a two-section cluster initial mass function, constant cluster formation rate, supervirial phase after a sudden expulsion of the remaining gas, and cluster mass loss due to stellar evolution and the clusters’ gradual destruction in the Galactic tidal field. The dynamical evolution model is based on previous N-body simulations. Results. The obtained tidal masses have been added to the MWSC catalogue. A general CMF (GCMF), built for all cluster ages around the Sun, has a bell-like shape and extends over four decades in mass. The high-mass slope found for tidal mass log mt/M⊙ ≥ 2.3 is equal to 1.14 ± 0.07. The CMFs for different age groups show the same high-mass slopes, while the low-mass slope is nearly flat for the youngest sub-sample (clusters younger than 20 Myr) and about −0.7 for the others. The inner and outer sub-samples covering Galactocentric radii R = 4.2–8.1 kpc and 8.9–13.5 kpc, respectively, are consistent with the GCMF, once the exponential decline of the Galactic disc density is taken into account. The model suggests star formation with low efficiency of 15–20%, where only 10% of stars remain bound in a cluster after gas expulsion and subsequent violent relaxation. The cluster formation rate required to reproduce the observed distributions in age and mass is about 0.4 M⊙ pc−2 Gyr−1. Conclusions. The obtained high-mass slope of the GCMF for the wide neighbourhood of the Sun is similar to slopes determined earlier in nearby galaxies for more luminous clusters with log m/M⊙ > 3.8. The MWSC catalogue supports models with a low star-formation efficiency, where 90% of stars are lost quickly after gas expulsion. The obtained cluster formation rate corresponds to open clusters’ contribution to the stellar content of the thin disc at the level of 30%.